Intercomparing the robustness of machine learning models in simulation and forecasting of streamflow

The human population makes use of global runoff up to 54% for various purposes such as consumption, extraction, and instream flow needs (Andreadis et al. 2007). Moreover, the estimation of global streamflow is highly uncertain because of limitations in observation and reachability. The simulation and forecasting of streamflow is a primary necessity in water resource planning and management (Hashim et al. 2016; Kersbergen 2016; Adnan et al. 2019b; Choubin et al. 2019). The forecasting of river flow with higher accuracy is essential for early hazard mapping and management which benefits a huge population and socio-economic activities (Wu & Chau 2013; Taormina & Chau 2015; Hussain & Khan 2020; Shamshirband et al. 2020). Further, the forecast will help in minimizing potential risks of flood and droughts, water supply for urban areas, irrigation planning for agricultural purposes, and also hydro-power projects (Londhe & Charhate 2010; Fotovatikhah et al. 2018; Adnan et al. 2020a; Homsi et al. 2020). An important issue in hydrological streamflow time-series prediction has been a greater concern in the past few decades.

Numerous models were proposed for forecasting and simulating the river discharge in various parts of the globe, especially data-driven models which had an upper hand over physical conceptual models due to their ease and computational efficiency (Wu et al. 2009; Diop et al. 2018; Adnan et al. 2019a; Alizamir et al. 2020). However, it is difficult to find a model that performs equally well for low-, medium-, and high-flow zones. Thus, the forecasting of streamflow becomes more complex and makes it difficult to create a real-time early warning system (Rezaie-Balf & Kisi 2018; Yaseen et al. 2019b; Adnan et al. 2020b; Li et al. 2020). In this concern, there is a need for a new forecasting approach that will be effective as well as efficient in predicting reliable and accurate data. In recent times, several researchers suggested that machine learning models predict streamflow with various significant approaches (Rezaie-balf et al. 2017; Kaya et al. 2019; Keum et al. 2020; Tikhamarine et al. 2020). These learning algorithms are data-driven models with the ability to learn the local environment and respond based on the scenarios with high accuracy.

In recent decades, various machine learning algorithms were proposed by researchers for predicting streamflow with decent performance. Previous studies suggested renowned machine learning techniques such as generalized linear model (GLM; Asong et al. 2016), partial least-squared regression (PLS; Matulessy et al. 2015), neural network (NNET; Coulibaly et al. 2005), K-nearest neighbor (KNN; Devak et al. 2015; Sekhar et al. 2018), and principle component regression (PCR; Sahriman et al. 2014), which are better for representing the local hydrological process. However, most of the machine learning techniques perform well in forecasting during the training period but fail to do the same in the testing period (Ghorbani et al. 2018; Yuan et al. 2018; Naganna et al. 2019; Yaseen et al. 2019a). The trick of handling bias and high variance in streamflow is still not resolved which clearly shows the overfitting issues associated with machine learning algorithms.

Though there are numerous machine learning techniques which perform better in streamflow projection, research scientists are facing issues in handling the drawbacks and improvising the model performance. Unfortunately, no technique overcomes all the drawbacks as we are still exploring methods to accurately model the local hydrological process. The present study proposes the Extreme Gradient Boosting Decision Tree (EXGBDT) approach for comparing its performance with other traditional models and validating it through the evaluation of various hydrological indices. The present study aims to predict river discharge with the help of daily weather parameters such as precipitation, average temperature, maximum temperature, and minimum temperature. The intercomparison of data-driven hydrological models was performed with renowned machine learning techniques and a proposed method to attain a low bias and variance in monthly streamflow prediction.

Numerous hydrological studies over the Indian subcontinent have previously been performed (Kale et al. 2010; Bhuvaneswari et al. 2013; Bhave et al. 2018; Arulbalaji & Padmalal 2020). However, most of the studies focused on the sub-basin-level and station-level discharge prediction. The current study deals with a large-scale river basin named Cauvery river basin located in southern peninsular India, which has frequent flood and drought issues. The study basin is one of the essential rivers in the southern part of India which provides water supply to a huge urban community for domestic use and enormous agricultural land area for irrigation purposes. Therefore, it is essential to model the streamflow and forecast the discharge pattern throughout the tributaries of the river basin. It is essential to build an individual model that performs equally well at low-, medium- and high-discharge stations to reduce the computational burden. Thus, an intercomparison of various machine learning model performances is carried out to select an optimum model and validated through the evaluation of multiple hydrological indices. The key objectives of the present study are (1) to improve the quality of observed hydrological time-series data by handling missing values and (2) to develop a hydrological model to perform equally well at low-, medium-, and high-flow zones at a large-scale river basin.

The current study was conducted over the Cauvery river basin, which is located over the southern peninsular region of the Indian subcontinent. The basin extends over 75°27′E to 79°54′E and 10°9′N to 13°30′N and lies over three states and one union territory. The river originates in Karnataka and meets the sea at Tamil Nadu passing through Kerala and Pondicherry. The total drainage area of the basin is 85,626 km², and the overall length of the river is 802 km. The boundary map representing the extent of the Cauvery river basin is presented in Figure 1. The river is confined by the Western Ghats and the Eastern Ghats on the west and east, respectively. The key portion of the river basin is concealed with cultivated land and forest, and it is also known as the rice bowl of South India. The water depletion in the basin has increased by up to 40% in the past few decades (Raju et al. 2013; Madolli et al. 2015). The risk of drought is high during the dry seasons, and the risk of flood is high during monsoon seasons in the basin area.

The Cauvery river basin is known for its tropical and sub-tropical climate zones where the north-west region is colder than the rest of the basin. The basin has four seasons, namely winter (December to February), summer (March to June), south-west monsoon (July to September), and north-east monsoon (October to November) (Bhuvaneswari et al. 2013; Madolli et al. 2015). The basin remains dry during summer and winter, which contributes a longer period of the year, and the monsoon season brings rainfall to the entire basin (Solaraj et al. 2010; Bhave et al. 2018). April is the hottest month, whereas January is the coldest month of the whole basin, and the average monthly temperature ranges from 18 to 33 °C (Nadu & Nadu 1981; Sunil et al. 2010). The basin is further classified into the upper, middle, and lower basins for a better comparison of climate variability and river flow discharge patterns within the basin. Further, it will help compare the different flow patterns in high-, medium-, and low-flow regions.

Meteorological data are essential for predicting the streamflow of the river basin. Meteorological datasets include daily precipitation (rainfall) and temperature (minimum, maximum, and average). There are three main organizations in India which record meteorological parameters which are (1) India Meteorological Department (IMD), (2) Central Water Commission (CWC), and (3) Indian Space Research Organization (ISRO) Automatic Weather Stations. CWC has established 35 stations located in the basin to recognize the atmospheric and river dynamics relationship. The hydro-meteorological and river flow data from these 35 daily observed stations positioned in the Cauvery river basin from 1951 to 2015 are collected. The description of the observation stations situated in the Cauvery river basin is presented in Table 1. The classification of the Cauvery river basin, observation stations, and river line is mapped in Figure 2. The details of station numbers provided in Figure 2 are explained in Table 1.

The historical observed data for the study area is collected concerning 35 observation stations from 1950 to 2015. Further, the entire time-series data are divided into the calibration period (1950–2000) and the validation period (2001–2015) for better consideration and evaluation of the model performance. The selected weather parameters and their short name, description, and units are presented in Table A1 (Appendix). The classification of the Cauvery basin into the upper, middle, and lower basins for a better comparison of river flow discharge patterns within the basin is illustrated in Figure 3. The framework adopted in this study is presented in the following section.

The proposed framework for building a data-driven hydrological model for simulating and forecasting streamflow in the Cauvery river basin is represented in Figure 4. The initial steps involve the collection of data for the study area which includes meteorological data and discharge data. The station-wise observed weather parameters (pr, tas, tasmax, and tasmin) are collected for the assigned baseline period of 1951–2005. For the same baseline period, the observed streamflow data for 35 stations along the Cauvery river basin are extracted. The collected discharge data are imputed for missing values using the weather data. Further, the collected data are divided into calibration (75%) and validation (25%) datasets, i.e. 1951–1990 and 1991–2005, respectively. Later, the data-driven models are built using the selected machine learning models and proposed models for comparison of performance. The performance of the various models is evaluated by various performance evaluation parameters such as normalized root-mean-squared error (NRMSE %), percentage bias (PBIAS %), Nash–Sutcliffe efficiency (NSE), and coefficient of determination (R²) for both calibration and validation periods. Further, the better performing model is selected based on the evaluation and hydrological indices which are calculated to compare with the actual observed data.

Insight into the streamflow model can be obtained by evaluating various hydrological statistics such as baseflow, high-, and low-spell statistics (Ladson et al. 2013; Ward 2013; Booker 2015). In this study, various hydrological indices which enlighten in-depth details of discharge at a selected basin were evaluated. Initially, the station-wise hydrological indices are calculated using the observed streamflow and later, these indices are compared with the simulated discharge to access the ability of the model in representing the local scenarios (Van Der Velde et al. 2013; Piras et al. 2016). Various hydrological indices considered and evaluated in this study using Hydrostats R package are given in Table A2 (Appendix).

The intercomparison of machine learning models in the robustness of simulation and forecasting of streamflow is performed. The datasets are processed as mentioned in the framework and model results are presented concerning models' calibration and validation for a better understanding of model performance. The performance of selected models and their ability in representing the local conditions are discussed in the following sections.

The historical station observed daily discharge and weather parameters considered in this study for the selected duration of 1951–2015 (65 years) are converted into time-series data. Further, the data are split into training data 1951–2000 (50 years) and testing data 2001–2015 (15 years). The interannual variability of observed data for precipitation and discharge for three different stations (Chunchunkatte, T.K.Halli, and Peralam from the upper, middle, and lower basins, respectively) from each sub-basin is presented in Figure 5. The plot clearly shows the annual trend precipitation and its respective discharge amount. There is a significant drop in discharge trend, especially in the lower Cauvery river basin over the past few decades. This is possibly due to rapid urbanization and amplified riverbed sand mining.

The streamflow for 35 observation stations is modeled using station observed precipitation, average, minimum, and maximum temperature data. The simulations were made using GLM, PLS, NNET, KNN, PCR, and the proposed EXGBDT model for the calibration period and predicted for the validation phase. The performance of each model is evaluated using the selected performance evaluation parameters and the observations are given in Table 2. The table compared the performance of each model at the calibration and validation phases. The evaluation parameters clearly state that the performance of models during the validation phase is slightly lower than the calibration. It is also evident that the proposed EXGBDT model performs exceptionally well compared to other machine learning models. The variance of the proposed model for the testing period is around 15% throughout the basin and bias is reduced to less than 6%. Further, the R² and NSE values are above 0.7, illustrating the model efficiency. The plot showing the intercomparison of streamflow simulation outcomes from various machine learning models is given in Figure 6. The monthly hydrograph of considered models was compared for sample high-, medium-, and low-flow stations from upper, middle, and lower basins. The hydrographs show a close association of EXGBDT model simulation, especially in peaks and fall throughout various discharge ranges.

The EXGBDT model is selected due to its advantages over other machine learning models for predicting the streamflow discharge at the Cauvery river basin. The model is built to simulate the discharge using training data and the same model is used to predict the discharge for the testing period. The outcome is signified in Figure 7 which illustrates the significance of the model at both calibration and validation phases. Further, the ability of the model in representing the local conditions is evaluated through various hydrological indices in the following section.

The comparison of hydrological indices for observed and modeled discharges over the Cauvery river sub-basins is given in Table 3. The daily discharge data are used to calculate these indices. The table gives the percentage of the variance between observed and model data at each index considering 35 stations. The percentage variance shows that the model is performing well in representing the baseflow statistics such as mean and median daily flow, mean baseflow volume, and index. Similarly, the model signifies high-spell and low-spell statistics with an acceptable variance in all sub-basins. The assessment of performance evaluation parameters and the evaluation of hydrological indices suggest that the proposed model is better at representing the local conditions. Consequently, the model can be suggested for forecasting future discharge projection for river basin-scale studies.

The intercomparison of streamflow simulation and prediction models using various machine learning techniques was conducted. A large-scale river basin located in southern peninsular India named Cauvery with frequent floods and drought problems was considered in this study. The daily streamflow discharge model was developed for 35 stations located in the basin using the daily observed precipitation, average, maximum, and minimum temperature. The performance of various machine learning models was evaluated and compared for model selection. Later, various hydrological indices were calculated for observed and predicted discharges for comparing and evaluating the replicability of local conditions.

The following conclusions were drawn from the study:

• (1)

  The model variance and bias of the EXGBDT are less than 15 and 5%, respectively, throughout the basin, which is the least compared with other machine learning techniques considered in this study.

• (2)

  The NSE and R² values are above 0.7 for both the training and testing phases which demonstrate the effectiveness of the model's performance.

• (3)

  The comparison of monthly observed and model-predicted discharges during the validation period illustrates the model's ability in representing the peaks and fall in high-, medium-, and low-flow zones.

• (4)

  The assessment and comparison of hydrological indices between observed and predicted discharges illustrate the model's ability in representing the baseflow, high-flow, and low-flow statistics.

Simulating streamflow and predicting discharge are essential for water resource planning and management especially in large-scale river basins. The proposed machine learning technique demonstrates significant improvement in model efficiency by dropping variance and bias, which in turn improves the replicability of local-scale hydrology. The present study considered streamflow discharge simulation of individual station projection and performance. However, simulation based on stream order is not performed in this study which can be considered as the future direction in improvement of the model performance.

All relevant data are included in the paper or its Supplementary Information.